Question

which of the following best describes the construction above?

a. ray ge bisects angle fgh
b. ray ge trisects angle fgh
c. ray ge is parallel to ray gh only
d. ray ge is parallel to ray gh and ray gf

Explanation:

Identify the geometric construction steps shown

The image shows an angle \(\angle FGH\) with vertex \(G\).

1. An arc is drawn centered at \(G\) intersecting rays \(GF\) and \(GH\).
2. Two intersecting arcs of equal radius are drawn centered at these intersection points.
3. A dashed ray \(GE\) is drawn from vertex \(G\) through the intersection of these two arcs.

Determine the purpose of the construction

This sequence of steps is the standard compass-and-straightedge construction used to bisect an angle. Therefore, ray \(GE\) bisects angle \(FGH\).

Match with the given options

• Option A states: "ray GE bisects angle FGH". This matches the identified construction.

Answer:

• (A) ray GE bisects angle FGH (Correct answer)
• (B) ray GE trisects angle FGH
• (C) ray GE is parallel to ray GH only
• (D) ray GE is parallel to ray GH and ray GF